The vertices of a triangle are labeled clockwise A(–5, 3), B(6, 1), and C(–2, –3). How could you show that the figure is a right
triangle?
1 answer:
Explanation:
When the points are plotted on a graph, it is easy to see that the slope of AC is -2 and the slope of BC is 1/2. These slope values have a product of -1, so the corresponding line segments are perpendicular to each other.
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If you have studied vectors, you can find the dot product of AC with BC:
AC = (-5, 3) -(-2, -3) = (-3, 6)
BC = (6, 1) -(-2, -3) = (8, 4)
The dot product is ...
(-3, 6)·(8, 4) = (-3)(8) + (6)(4) = -24+24 = 0
When the dot product of vectors is zero, they are perpendicular.
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Answer:
24 ft cubed
Step-by-step explanation:
The volume of a rectangular prism is denoted by the formula: , where
is the length, w is the width, and h is the height.
Looking at the diagram, we can see that the length is 2 ft (so = 2), the width is 4 ft (so w = 4), and the height is 3 ft (so h = 3). Now, we can just plug in these values to find V, the volume:
Thus, the answer is 24 ft cubed.
Hope this helps!